I totally agree with WannaBe "Three late mornings isn't persistent lateness – even, shock horror, 4! Certainly not a justification to stop overnight contact midweek."
Red has posted some excellent points.
In the long run this may well be far more harmful than occasionally being late for school, IMHO (which I kind of feel you are not really interested in despite posting in AIBU).
Having and operating an alarm clock at age 8 is not a terrible thing or a tragedy.
I do wonder why your daughter is so worried about being 5 minutes late If she is getting very stressed about being just a little bit late that seems to me there may be other issues there. How long ago was the divorce (don’t answer if you do not wish to). I think you are projecting some stress here.
Your ex is in the wrong here, definitely, but IMHO YABU to consider stopping the kids staying over midweek and to potentially rock the boat of having a good co-parenting relationship over this issue.
I would be very shocked if the school thought making such an issue of this were worth it if they realised the potential ramifications. By all means talk to the school, and get your ex involved, but try not to turn this into a blame game.
Homemaker re "It really doesn't matter how late she is." This is coming across as your issue, you feeling bad she is late and I really do wonder if she is picking up on this from you.
I know you are upset and cross. Are there other issues here? I know you said he shouted and that is wrong, totally, and maybe some of this is reminding you why you split up and is exacerbating issues from the past?
Please do not allow this to take on a bigger part of your lives than it needs to.
You will regret it if you allow this to spoil an otherwise good working relationship of co-parenting. Especially at this time of year, you will upset the kids, yourself and your dh, and really truly those 5 minutes late at school are of so little significance.
YES your ex is in the wrong to make dd late but you are also in the wrong if you allow this to become a competition on good parenting and make it such a massive issue.
This could be what you tell your dd - that she can take some control of the situation (alarm clock, totally fine) and being a bit late occasionally, (totally fine) and her dad has flaws but don’t we all.
Because the message you are giving here potentially, if you exacerbate this, is her dad is not good enough (for you, for her) because he is occasionally getting her to school a tiny bit late.
Plus you are being goaded on by people here who have an equally unreasonable opinion of lateness. Lateness is cultural, lateness is not the issue you are making it. Stop and think and reassess, please.